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The entire experience of getting users into a new application and familiar with how to use it is referred to as "User Onboarding."
This process can include tutorials, how-to graphics & animations, or buttons & notifications pointing out new features. This is often a first-time/one-time thing, but users can usually access the content through a ...

I think JeromeR has covered quite a few names for the button. We used "Get me started" for our website. The particular behaviour is often called "Web Tour" or "Guided Tour". Related JS plugin links - Bootstrap Tour , IntroJS

The name of that button could be anything appropriate to the users you're addressing. it could be:
New here?
Show me
Take a tour
Important
3 quick things
and so on.
A related question you might want to ask is this: What is the name of this process of welcoming and user-instruction? This concept has a name: first experiences.
First experiences
...

Search for "feature tour" and you will find a number of good options. Include the language/framework of your platform, and you will likely find a plugin or library that will help you create a feature tour.

You can google for "Onboarding Overlay Screen" or "Onboarding Coach Marks". Try looking at the image results for a quick overview and sample screenshots.
Overlays and coach marks are almost always used together where the overlay is a screen casted over the rest of the screen while maintaining the spotlight on any one of the features. Coach marks are ...

You're wondering whether the question-mark icon is universally recognised. There are two parts to this:
Do your users have prior experience with a question-mark icon?
Will your users recognize YOUR question-mark icon as offering Help?
I can only answer the first question. I did a quick search of the various style guides. To sum up:
The Microsoft ...